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Measurement of Financial Risk Persistence

  • Cornelis A. Los

    (Kent State University)

This paper discusses various ways of measuring the persistence or Long Memory (LM) of financial market risk in both its time and frequency domains. For the measurement of the risk, irregularity or 'randomness' of these series, we can compute a set of critical Lipschitz - Hölder exponents, in particular, the Hurst Exponent and the Lévy Stability Alpha, and relate them to the Mandelbrot-Hoskings' fractional difference operators, as occur in the Fractional Brownian Motion model (which is our benchmark). The main contribution of this paper is to provide a compaison table of the various critical exponents available in various scientific disciplines to measure the LM persistence of time seies. It also discusses why Markov- and (G)ARCH models cannot capture this LM, long term dependence or risk persistence, because these models have finite lag lengths, while the empirically observed long memory risk phenomenon is an infinite lag length phenomenon. Currently, there are three techniques of nonstationary time series analysis to measure time - varying financial risk: Range/Scale analysis, windowed Fourier analysis, and wavelet MRA. This paper relates these powerful analytic techniques to classical Box-Jenkins-type time series analysis and to Pearson's spectral frequency analysis, which both rely on the uncorroboated assumption of stationarity and ergodicity.

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File URL: http://128.118.178.162/eps/fin/papers/0502/0502013.pdf
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Paper provided by EconWPA in its series Finance with number 0502013.

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Length: 37 pages
Date of creation: 13 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpfi:0502013
Note: Type of Document - pdf; pages: 37
Contact details of provider: Web page: http://128.118.178.162

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  1. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  2. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  3. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
  4. Sutthisit Jamdee & Cornelis A. Los, 2004. "Long Memory Options: Valuation," Finance 0409049, EconWPA.
  5. Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
  6. Cornelis A. Los, 2004. "Nonparametric Efficiency Testing of Asian Stock Markets Using Weekly Data," Finance 0409033, EconWPA.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Akgiray, Vedat, 1989. "Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts," The Journal of Business, University of Chicago Press, vol. 62(1), pages 55-80, January.
  9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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